Trigonometric Identities Question 12
Question: $ \tan 5x\tan 3x\tan 2x= $
[EAMCET 1991]
Options:
A) $ \tan 5x-\tan 3x-\tan 2x $
B) $ \frac{\sin 5x-\sin 3x-\sin 2x}{\cos 5x-\cos 3x-\cos 2x} $
C) 0
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
We have $ 5x=3x+2x\Rightarrow \tan 5x=\tan (3x+2x) $
Þ $ \tan 5x=\frac{\tan 3x+\tan 2x}{1-\tan 3x\tan 2x} $
Þ $ \tan 5x-\tan 5x\tan 3x\tan 2x=\tan 3x+\tan 2x $
Þ $ \tan 5x\tan 3x\tan 2x=\tan 5x-\tan 3x-\tan 2x $ .
BETA
